Question: Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of $4.5$ milliliters per second. After $17$ seconds, $148.5$ milliliters of slushy remained. How much slushy was originally in the cup?
Explanation: Mariana drank $4.5$ milliliters of slushy each second, so she drank $4.5T$ milliliters in $T$ seconds. The remaining amount of slushy is found by taking the original amount and subtracting from it the amount Mariana had already drunk. We can express this with the equation $R=S-4.5T$, where: $R$ represents the remaining amount of slushy to drink at a given time (in milliliters) $S$ represents the original amount of slushy (in milliliters) $T$ represents the time (in seconds) We want to find $S$, so let's first solve the equation for $S$ : $ \begin{aligned}R&=S-4.5T\\ S&=R+4.5T\end{aligned}$ Now, we know that after $17$ seconds $(T={17})$, $148.5$ milliliters of slushy remained $(R={148.5})$. Let's plug these values into the equation to find the value of $S$. $ S={148.5}+4.5\cdot{17}=225$ Therefore, there were originally $225$ milliliters of slushy in the cup. To find how long it took Mariana to drink all the slushy, we can plug $R=0$ into the equation and solve for $T$. $ \begin{aligned}225&=0+4.5T\\ 4.5T&=225\\ T&=50\end{aligned}$ There were originally $225$ milliliters of slushy in the cup. It took Mariana $50$ seconds to drink all the slushy.